设2006x^3=2007y^3=2008z^3=S^3
则2006=s^3/x^3,2007=s^3/y^3,2008=s^3/z^3.
左边=【2006x^2+2007y^2+2008z^2】开三次方[(1/x+1/y+1/z)s^3]开3次方=s*(1/x+1/y+1/z)开3次方
右边=s/x+s/y+s/z=s(1/x+1/y+1/z)
所以有:s*(1/x+1/y+1/z)开3次方=s(1/x+1/y+1/z)
所以得:1/x+1/y+1/z=1